Single-stage vehicles using air-breathing propulsion hold promise for more economical delivery of payloads to orbit. The characterization of minimum-fuel trajectories over the range of possible engine and aerodynamic performance of such vehicles provides useful feedback to engine and vehicle designers and paves the way for the development of guidance logic. In this paper, the minimum-fuel trajectory problem is formulated, propulsion system and aerodynamic models are presented, a numerical solution approach is described, and some preliminary results are discussed.